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The density of the ISE and local limit laws for embedded trees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2006 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 16, no 3, 1597-1632 p.Article in journal (Refereed) Published
Abstract [en]

It has been known for a few years that the occupation measure of several models of embedded trees converges, after a suitable normalization, to the random measure called ISE (integrated SuperBrownian excursion). Here, we prove a local version of this result: ISE has a (random) Milder continuous density, and the vertical profile of embedded trees converges to this density, at least for some such trees.

As a consequence, we derive a formula for the distribution of the density of ISE at a given point. This follows from earlier results by Bousquet-Melou on convergence of the vertical profile at a fixed point.

We also provide a recurrence relation defining the moments of the (random) moments of ISE.

Place, publisher, year, edition, pages
2006. Vol. 16, no 3, 1597-1632 p.
Keyword [en]
random binary tree, natural labeling, vertical profile, ISE, local limit law
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-22673DOI: 10.1214/105051606000000213ISI: 000241428300019OAI: oai:DiVA.org:uu-22673DiVA: diva2:50446
Available from: 2007-01-19 Created: 2007-01-19 Last updated: 2017-12-07Bibliographically approved

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Janson, Svante

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